Why do purgers wear masks?

The problem being, yeah you can do what you want on that night, but if people know who you are they might try to get you back on the following purge.

The way I see it, they're expressing (or "purging") their inner evil through the ugly masks they wear. This is all about letting loose with all your criminal desires, so if these people have been hiding their intentions until the day of the purge, the real mask they wear is their actual face. The face they wear during the purge is an expression of their inner-self.

Also, since they're preying on innocent victims they probably want to scare them as much as possible, hence why the masks are often vulgar and threatening.

Because even if it's legal, maybe you don't want people knowing you're a murderer, rapist, or criminal for the next 364 days.

A pathetic attempt to make the psychopaths look intimidating.

It's simple why they wear the masks: They see the Purge as Adult Halloween

Why are you here if you haven't seen the movie yet?

There are many reasons why people wear masks. Some wear them for their own amusement, others to scare people. Still more, to conceal their own identity or as a social bonding activity, like on Halloween.

There are no problems that cannot be solved with a can of brake clean and a lighter

Even lawful actions have consequences.